Let's say you are not pleased with the way someone handled a situation. In that case, you would offer a reproof, or a criticism, of what they did. So if you reproof someone, you pretty much chew them out.
From the Late Latin reprobāre, which means "to disapprove of," the word reproof has a pretty clear meaning. The added meaning of "shame or disgrace" came later. Reproof is a not feel-good word, as you know if you've ever been on the receiving end of a verbal reproof. English Poet Walter Savage Landor described, once wrote “An ingenuous mind feels in unmerited praise the bitterest reproof.” Poets are so hard to please.